Theorems · Theorem · functional analysis

OrthonormalBasis.equiv_apply_euclideanSpace

∀ {ι : Type u_1} {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : Fintype ι] (b : OrthonormalBasis ι 𝕜 E) (x : EuclideanSpace 𝕜 ι),
  ((EuclideanSpace.basisFun ι 𝕜).equiv b (Equiv.refl ι)) x = ∑ i, x.ofLp i • b i

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

1 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintype